Whither Applied Mathematics at Leaving Certificate?
by Maurice OReilly, St Patrick’s College, Drumcondra
delivered at Waterford Institute of Technology, 17th April, 2002
In this paper, I hope to set a draft agenda addressing the question in the title. My
objective is to set a ball in motion and not necessarily on a frictionless plane. I hope this
ball will neither come, after a few predictable bounces, to an early state of rest nor
oscillate without purpose at the end of a spring. Perhaps this modest impulse will produce
a reaction? I hope not equal and opposite, since applied mathematics is surely more than
Newtonian mechanics!
I suspect many of you took the applied maths paper in the Leaving. What are your
memories of it? I took it in 1973. The course was not taught in my school and so I
managed with four resources: Humphrey & Topping, Lambe (was it the metric version?),
Bowman’s Calculus and help, at crucial moments, from my older brother who, at the
time, was in his second year of electrical engineering in ‘Merrion Street’. I recall that the
tough part was interpreting the question, the rest was fairly, well, mechanical, involving
algebra and calculus. The techniques for solving differential equations (up to second
order linear) were interesting extensions of material familiar from the regular maths
course, but quite disconnected from ‘applications’. In reviewing the material now, I
realise that, in the absence of a teacher, I spent some time studying material which was
not at all on the syllabus!
With that brief personal introduction, let me turn to how I intend to approach the question
posed. There will be three parts:
1. Current situation
2. Possible developments
3. Concluding remarks
As already suggested, none of this is intended to be conclusive nor even authoritative as
far as it goes.
1. Current situation
To begin, let us consider how Applied Mathematics results compared with those of other
subjects in the 2001 Leaving Certificate Examination (LCE). In particular, let us consider
measures of skewness for twenty subjects (the 19 most popular together with Applied
Mathematics). We use the frequencies for each letter grade (A-F) to calculate an
empirical probability distribution for performance in each subject, and calculate
  X   3 
2
2
E 
  from this, where   E  X    and   E X  .
   




Whither Applied Mathematics at Leaving Certificate?
page 1
Here are the results at Higher Level, in increasing order of skewness:
LCE 2001 (Higher Level) - skewness
English
-0.1924
History
French
-0.1470
Tech Drawing
Art
-0.0521
Engineering
Irish
0.0084
Chemistry
Geography
0.0373
Economics
German
0.0707
Mathematics
Physics
0.1333
Accounting
Home Econ (S+S) 0.1382
Applied Math
Biology
0.1416
Construction
Business
0.1676
Music
0.1925
0.2004
0.2267
0.2425
0.2924
0.3262
0.3278
0.3325
0.5981
1.1440
Generally speaking, we see that grades are skewed to the left (that is towards higher
grades), Music being the most positively skewed. Applied Mathematics is quite
positively skewed, at the far end of the scale from English.
The results at Ordinary Level are:
LCE 2001 (ordinary level) - skewness
English
0.0711
Physics
Biology
0.0983
Geography
Applied maths
0.1105
Art
Mathematics
0.1153
French
History
0.1570
Business
Tech drawing
0.1613
Engineering
Economics
0.1752
Irish
Accounting
0.1781
German
Chemistry
0.1883
Construction
Home Econ (S+S) 0.2106
Music
0.2250
0.2312
0.2824
0.3629
0.4069
0.4537
0.5392
0.5610
0.7445
1.1231
Here again, the extremes are represented by English and Music, while Applied
Mathematics is relatively unskewed. However the Applied Mathematics and History
results are unusual in that the number of A grades is greater than that of any other grade;
for these two subjects, skewness as an indicator fails to capture their unusual grade
profile.
Applied Mathematics as a subject in the senior cycle of our second level education
system is grouped (by the Department of Education and Science) along with five other
subjects, Mathematics, Physics, Chemistry, Physics & Chemistry (combined) and
Biology, in the ‘Science Group’ [Dept. of Education]. On the other hand, the NCCA
website states that, ‘There are at present five Leaving Certificate science subjects:
Biology, Chemistry, Physics, Agricultural Science, and Physics and Chemistry
(combined). The NCCA has completed a revision of the first four of these syllabuses and
has prepared a consultation draft syllabus for Physics and Chemistry (combined).’
[NCCA]
Whither Applied Mathematics at Leaving Certificate?
page 2
The Mathematics syllabus has also been revised (since the mid-nineties), leaving Applied
Mathematics somehow forgotten. This neglect is perhaps understandable if not excusable.
In contrast to the other subjects mentioned, Applied Mathematics is neither core (in the
sense of Mathematics itself) nor has it been pushed high on the educational agenda
because of the ‘crisis in science’. Moreover, participation in the LCE, in Applied
Mathematics (ranked 22nd out of just over thirty subjects in 2001) was less than half that
of Agricultural Science, the least popular (apart from Physics & Chemistry combined) of
the other subjects mentioned.
Subject
Mathematics
Biology
Physics
Chemistry
Agricultural Science
Applied Mathematics
Physics & Chemistry
No. of Students
(2001, at all levels)
55144
24061
8411
6356
2915
1371
1023
Popularity
Rank
1
7
12
16
20
22
23
Two comprehensive longitudinal studies of candidates sitting the Junior Certificate
Examination (JCE) in 1994 offer invaluable insights into participation and performance
in all subjects at second level [Millar 1999, 1998]. We shall extract from these, material
relating to Applied Mathematics.
Cohort
LCE 1996
LCE 1997
neither of these
Male
16443
9111
7841
Female
16776
11844
4993
Total
33219
20955
12834
Our investigation includes the first two of these cohorts. It is reasonable to assume that
the vast majority of the LCE 1997 cohort took the Transition Year Option (TYO) at the
beginning of the Senior Cycle.
Let us turn our attention first to the question of gender bias and participation in science
subjects. The participation rates of the LCE 96 cohort (as percentages of all males, all
females and all students, respectively) were:
biology
maths
chemistry
ph & ch
physics
app maths
agr sc
M
35.1%
99.8%
13.5%
4.1%
25.5%
3.4%
8.9%
F
64.9%
99.9%
12.0%
1.6%
7.9%
0.4%
1.0%
Whither Applied Mathematics at Leaving Certificate?
Total
50.1%
99.9%
12.7%
2.8%
16.6%
1.9%
4.9%
page 3
The participation rates of the LCE 97 cohort were:
M
biology 37.2%
maths
99.8%
chemistry 14.6%
ph & ch 2.3%
physics 25.7%
app maths 5.9%
agr sc
5.7%
F
62.5%
99.9%
13.0%
0.9%
9.5%
1.4%
0.9%
Total
51.5%
99.9%
13.7%
1.5%
16.5%
3.3%
3.0%
For each cohort, we note that females participate more than males in Biology, both
participate equally in Mathematics, while males participate more than females in the
other five subjects. In Applied Mathematics, male participation is greater by a factor of
between 4.8 (LCE 97) and 7.5 (LCE 96). The tables underscore disparities which are
hardly surprising for those with a modest acquaintance with issues in science education in
Ireland. It is interesting to note the marked increase in participation in Applied
Mathematics among those who took the TYO: a factor of 1.8 for males and 3.0 for
females. Moreover, taking the TYO has lessened the gender disparity (in Applied
Mathematics) by 42%. Generally speaking, the TYO is good for science participation
(including reduction of gender bias), and especially good for participation in Applied
Mathematics.
To emphasise this point further, let us look at participation rates in Applied Mathematics
(at higher and ordinary levels) across the four school types (secondary, vocational,
comprehensive and community):
LCE 96
sec
voc
comp
comm
all schools
H
2.22%
0.45%
1.06%
1.03%
1.67%
O
0.25%
0.09%
1.06%
0.05%
0.21%
population
21194
6892
849
4284
33219
LCE 97
sec
voc
comp
comm
all schools
H
3.67%
0.92%
4.04%
1.71%
3.06%
O
0.26%
0.03%
2.31%
0.19%
0.27%
population
15123
3150
520
2162
20955
Again, students taking the TYO have substantially increased participation rates.
Whither Applied Mathematics at Leaving Certificate?
page 4
Let us turn now to the question of students’ achievement in science in the LCE. The
following tables show (for each cohort) the percentages of low achievers (with grades E,
F or NG) in the seven science subjects:
LCE 96
maths
app maths
physics
chemistry
ph & ch
biology
agr sc
H
3.6%
8.1%
14.8%
13.3%
14.6%
12.5%
5.3%
O
15.3%
19.7%
22.4%
22.2%
34.5%
19.1%
26.4%
LCE 97
maths
app maths
physics
chemistry
ph & ch
biology
agr sc
H
2.8%
8.4%
10.2%
8.2%
8.3%
8.2%
4.0%
O
9.3%
7.1%
19.0%
13.6%
29.4%
14.2%
13.5%
Apart from negligible differences at Higher Level in Mathematics, Applied Mathematics
and Agricultural Science, the figures show substantially better performance by students
taking the TYO.
Next, let us consider the Applied Mathematics data on its own as far as choice of
examination level, participation by gender and participation in the TYO are concerned.
We ask four questions and, for each, display the relevant data and draw a conclusion
(quoting a p-value arising from the appropriate hypergeometric distribution).
Question 1: Does the choice of examination level (higher or ordinary) depend on
participation in the TYO?
H
O
96
555
71
626
97 (TYO)
642
56
698
1197
127
1324
Conclusion 1: There is some evidence for such dependence (p = 0.0416).
Whither Applied Mathematics at Leaving Certificate?
page 5
Question 2: Does participation in the TYO depend on gender?
96
97
M
551
538
1089
F
75
160
235
626
698
1324
Conclusion 2: The evidence for such dependence is overwhelming (p < 0.000001).
Question 3: For those participating in the TYO, does the choice of examination level
depend on gender?
H
O
M
489
49
538
F
153
7
160
642
56
698
Conclusion 3: There is some evidence for such dependence (p = 0.0462).
Question 4: For those not participating in the TYO, does the choice of examination level
depend on gender?
H
O
M
486
65
551
F
69
6
75
555
71
626
Conclusion 4: There is no evidence for such dependence (p = 0.3406).
We note that similar tests indicate that participation of male and female students does not
depend on whether a student attends a co-educational or single sex school.
An indicator of (poor) performance is the proportion of students who achieve a low grade
(E, F or NG). When we examine how strongly this performance indicator depends (in the
case of Applied Mathematics) on gender, participation in the TYO and choice of
examination level, we see some evidence for such dependence on choice of examination
level alone (p = 0.0362):
Low
Not low
H
99
1098
1197
O
18
109
127
Whither Applied Mathematics at Leaving Certificate?
117
1207
1324
page 6
This dependence is accentuated (p = 0.004559), however, if we restrict our attention to
students taking the TYO:
Low
Not low
H
45
510
555
O
14
57
71
59
567
626
Twenty-five other investigations were carried out in a similar fashion, however the
results were either not statistically significant or did not lead to a significant
interpretation.
Turning now to the content and style of examination papers at Higher Level, we see that
the content today is just as it was thirty years ago, although the style has changed to some
extent. Here are typical topics covered by the ten questions:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Motion under piecewise constant acceleration
Balls in projection or hopping
Constant velocity in two dimensions
Forces and motion involving pulley systems
One particle in simple harmonic motion
Systems of two particles in equilibrium or in collision
Forces acting on rods in equilibrium (perhaps involving friction)
Rotating discs and moments of inertia
Simple first order differential equations
(with applications to motion under resistance)
10. Forces acting on a submerged body
Most LCE questions nowadays are clearly split into two parts, a manageable part (a) and
a more challenging part (b). Diagrams accompany questions where there had been none
before.
To understate the situation, the content is fossilised and represents only a tiny part of
what is normally considered as applied mathematics in the world outside the LCE. The
style has been modified to some extent over the years so as to make the paper more
student-friendly without compromising standards.
Anecdotal evidence strongly suggests that, in general, students who take Applied
Mathematics enjoy it greatly. The syllabus introduces them to problem-solving
techniques. Most of them are motivated to take the subject because they perceive it as a
useful introduction to anticipated studies in engineering. The focus provided by a
syllabus with a rather narrow scope is seen by some to be a significant strength. Students
who have high mathematical ability see the subject as an efficient points earner.
A welcome development in the mid-eighties was the publication of Murphy’s text
[Murphy] on applied mathematics. This nicely illustrated book supports the syllabus well.
Whither Applied Mathematics at Leaving Certificate?
page 7
It appears that this is the only book specifically written for Leaving Certificate Applied
Mathematics. In practice, it seems that many teachers rely on a variety of sources for
material, in particular texts for A-Level published in Britain.
In 1998, the Victor W Graham Perpetual Trophy was awarded from the first time. This
attractive trophy is awarded annually by the Institute for Numerical Computation and
Analysis to a teacher for achievement in Applied Mathematics [OReilly (website)].
2. Possible developments
My starting point is to acknowledge a blurring of the boundaries between ‘pure’ and
‘applied’ mathematics. According to Hersh, “A philosophy of mathematics that ignores
applied mathematics, or treats it as an afterthought, is out of date. The relationship
between pure and applied mathematics is a central philosophical question. A philosophy
of mathematics blind to this challenge is inadequate” [Hersh, p26]. This is a far cry from
the notion of ‘pure’ mathematics expounded by Russell or Hardy of 85 or 62 years ago.
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty
cold and austere, like that of a sculpture, without appeal to any part of our weaker
nature, without the gorgeous trappings of painting or music, yet sublimely pure, and
capable of a stern perfection such as only the greatest art can show.” [Russell, p63]
“I have never done anything ‘useful’. No discovery of mine has made, or is likely to
make, directly or indirectly, for good or ill, the least difference to the amenity of the
world.” [Hardy, p150]
In our view of the relationship between ‘pure’ and ‘applied’, we need to acknowledge
different approaches. Let me add a fourth point of view to those already quoted: “We
should … let mathematics be, just as other disciplines are, the pursuit of ways of seeing,
the pursuit of visions. We should teach our students to look for mathematical analogies,
to delight in them when they find them, to stretch them and test them and savor them …”
[Wales, in White, p33]
I maintain that those who are involved, collaboratively, in putting a syllabus together, as
well as those actually teaching applied mathematics should be as much aware of the
extreme points of view regarding the subject, as they are of the possibility to achieve a
middle way which is coherent, yet acknowledges nuance.
How might we construct a rationale for applied mathematics courses in our secondary
schools? For a start, I recommend a prominent place for the following elements: (a)
modelling, (b) problem-solving and (c) the ‘Rule of Three’ combined with the ‘Way of
Archimedes’. These elements need to be underpinned by informed practice in curriculum
design which (d) offers material at a level which is reasonably challenging, yet not
excessively difficult, (e) accommodates and distinguishes between Higher and Ordinary
Levels, and (f) is cognisant of other Senior Cycle courses such as Mathematics and
Physics.
Whither Applied Mathematics at Leaving Certificate?
page 8
The heart of applied mathematics must surely be modelling. It is reasonable to consider
this as a three-stage process, involving, according to Edwards & Hanson, problem
description, procedure and follow-up [Edwards, §2]. O’Donoghue has developed a
“tentative classification of applied problems for teaching purposes” involving two levels
of classification: “noise” and “domain of application” [O’Donoghue, in Cawley, p50].
Attention to problem-solving in the spirit of Polya provides a practical yet unifying
approach to tackling modelling (and more besides). In 1945, he proposed a framework
involving four phases: understanding the problem, devising a plan, implementing the plan
and reviewing the work [Polya]. This approach has been used, extended and refined by
many [Tall, p18, for example].
The ‘Harvard Consortium’, led by Hughes-Hallett and Gleason, prescribe two cures. The
first, for the restoration of mathematical content to calculus, is the Rule of Three: Every
topic should be presented geometrically, numerically, and algebraically. The second, for
the restoration of practical understanding, is the Way of Archimedes: Formal definitions
and procedures evolve from the investigation of practical problems [Hughes-Hallett].
Curriculum issues are always challenging. The NCCA has identified clearly many issues
affecting curriculum development for the science subjects [NCCA] including:





the role of science in society embracing both cultural and economic aspects
concern for declining popularity of the physical sciences
inadequate emphasis on issues such as analysis, synthesis and evaluation
a lack of congruence between assessment and syllabus aims & objectives
an unacceptable level of low achievement in science at Ordinary Level
In all of this, Applied Mathematics does not arise once in the discussion.
Including material which is sufficiently challenging and which stimulates interest and
curiosity is very important. At the same time, material should be reasonably accessible.
These aspirations hold equally at both Higher and Ordinary Level, but need to be
interpreted appropriately at each level. It is inappropriate to address any detail of these
issues in this paper, such detail being part of the distillation process.
Interest and curiosity can, and must, be stimulated, first and foremost, by expanding the
scope of Applied Mathematics as a subject in the Senior Cycle, way beyond its present
narrow confines of a corner of mathematical physics. Here are some areas where such
expansion might be established:
Whither Applied Mathematics at Leaving Certificate?
page 9












linear & nonlinear laws in many contexts
engineering & science – pollution, heat transfer
business – compound interest
computing – logic, networks
demography – population models
food safety – risk analysis
probability & statistics
meteorology
codes & cryptography
geometry & construction
astronomy
historical development – especially in Ireland
It would without doubt be over-ambitious to include many of these topics in a terminal
examination, however there is no reason why they should not be included appropriately
in project work complementing the examination. There is certainly scope for project
work, giving an opportunity for students to explore some particular field in greater depth
and over a reasonably long period.
In addition to mechanics, new or extended areas of content might include: differential
equations, difference equations, vector algebra, trigonometry, graph theory, data
handling, simulation and numerical analysis. Of these, differential equations are
especially important since they are at the core of mathematical modelling. Some of these
areas (especially the last three) are amenable to treatment in the environment of a
computer application package such as Excel or even Maple.
Differential equations as a single area admits treatment of a great variety of accessible
applications. The Harvard Consortium’s Calculus [Hughes-Hallett] includes the
application of differential equations in the following areas:
speed of learning
population models
interest compounded continuously
pollution in lakes
heating and cooling
radioactive isotopes
formation of ice
net worth of a company
velocity and acceleration
concentration of chemicals
expansion of the universe
income distribution in society
diseases and epidemics
predator-prey models
arms race in the Cold War
pendulums and oscillating springs
Although the development of models involving differential equations may in many cases
be too ambitious, more accessible models involving difference equations might well be
considered.
Whither Applied Mathematics at Leaving Certificate?
page 10
Some of the areas mentioned are already treated, to a greater or lesser extent, in the
Mathematics and Physics curricula. These include probability and statistics, as well as the
treatment of linear and nonlinear laws. It is possible that other areas (such as logic) may
be introduced in a future ICT/computing curriculum. Care is needed to ensure that
boundaries between subjects are clear, and that where there is any overlap that this is to a
purpose. Another cross-curricular aspect requiring attention is the question of how much
knowledge of the Mathematics curriculum is required for Applied Mathematics and,
indeed, the related logistical issue of topic scheduling between these two courses. For
example, a knowledge of integration is necessary for treatment of all but the simplest
differential equations, but integration is usually covered late in Senior Cycle
Mathematics.
The cultural and historical context in which mathematics finds itself is attracting
increased attention. It is of particular interest that this is happening in an Irish setting [e.g.
Bowler, Houston] as well as internationally [e.g. Acheson, Grattan-Guinness, Maor]. In
addition to the philosophical context mentioned earlier, it is important that curricular
development is informed by recent cultural and historical discourse also.
Many of the issues relating to the transition of students from second to third level
education mathematics in Ireland deserve attention in the current discussion, although it
should be noted that published material usually emphasises the entire population entering
third level, rather than the ‘elite’ who take Applied Mathematics [Brennan, Evans,
OReilly (2001)].
A vital over-riding consideration in any radical overhaul of the Applied Mathematics
syllabus is its acceptability by both students and teachers. Quite apart from the interest
inherent in the content of a new syllabus, these two groups must be convinced that the
effort put into fulfilling the requirements of a new syllabus are reasonable and that its
sense of purpose – not least as far as further study is concerned – is coherent.
Whither Applied Mathematics at Leaving Certificate?
page 11
3. Concluding remarks
As indicated at the beginning of this paper, we have tried to set a draft agenda for the
direction of Applied Mathematics as a Leaving Certificate subject. There are certainly
many issues to which inadequate attention has been paid. On the other hand, original
interpretations have been offered for some data.
Let us summarise the main findings and observations:
1. The profile of results by grade for Applied Mathematics is atypically skewed towards
higher grades (at both Higher and Ordinary Levels).
2. Applied Mathematics has not been considered as part of the ‘science family’ in recent
efforts to address the ‘crisis in science’.
3. A significant review of the syllabuses in Applied Mathematics has not taken place for
at least three decades.
4. The scope of the two syllabuses in Applied Mathematics is, at present, very restricted.
5. A focussed introduction to problem-solving in the context of engineering is a
significant strength of the Applied Mathematics syllabus.
6. Ranking 22nd, Applied Mathematics is not a particularly popular subject.
7. Male students participate in Applied Mathematics substantially more than do female
students.
8. Participation in the Transition Year Option (TYO) is good for science subjects
generally, and for Applied Mathematics in particular. It increases levels of
participation, reduces gender bias, and, at Ordinary Level, improves performance.
The reduction in gender bias here, as far as participation is concerned, is offset by the
fact that female candidates taking Applied Mathematics after the TYO are less
inclined to take it at Higher Level than are male candidates.
9. As in other subjects, poor performance in Applied Mathematics is more in evidence at
Ordinary Level than at Higher Level, and particularly so for those having taken the
TYO.
In addressing how Applied Mathematics might be developed, we emphasised the
following:
10. The broad philosophical, cultural and societal context of both Applied Mathematics
and the students studying the subject.
11. The central position of modelling, problem-solving and, perhaps, differential
equations in any syllabus in Applied Mathematics.
12. Attention to good practice in curriculum design.
13. A judicious balance between accessibility and challenge in the material of the
syllabus.
14. Expansion of the scope of this material, allowing for the possibility of project work.
15. Prerequisites and overlaps with other syllabuses.
16. Transition to third level studies.
17. Overall acceptability by students and teachers alike.
Whither Applied Mathematics at Leaving Certificate?
page 12
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Whither Applied Mathematics at Leaving Certificate?
page 13
Technical & Numerical Details
Calculation of skewness:
We use the frequencies for each letter grade (A-F) to calculate an empirical probability
  X   3 
distribution for performance in each subject, and calculate E 
  from this,
   




where  2  E  X   2 and   E X  .
Results at Higher Level, in increasing order of skewness:
LCE 2001 (Higher Level) - skewness
English
-0.1924
History
French
-0.1470
Tech Drawing
Art
-0.0521
Engineering
Irish
0.0084
Chemistry
Geography
0.0373
Economics
German
0.0707
Mathematics
Physics
0.1333
Accounting
Home Econ (S+S) 0.1382
Applied Math
Biology
0.1416
Construction
Business
0.1676
Music
0.1925
0.2004
0.2267
0.2425
0.2924
0.3262
0.3278
0.3325
0.5981
1.1440
The results at Ordinary Level:
LCE 2001 (ordinary level) - skewness
English
0.0711
Physics
Biology
0.0983
Geography
Applied maths
0.1105
Art
Mathematics
0.1153
French
History
0.1570
Business
Tech drawing
0.1613
Engineering
Economics
0.1752
Irish
Accounting
0.1781
German
Chemistry
0.1883
Construction
Home Econ (S+S) 0.2106
Music
Whither Applied Mathematics at Leaving Certificate?
0.2250
0.2312
0.2824
0.3629
0.4069
0.4537
0.5392
0.5610
0.7445
1.1231
page 14
Participation in ‘science’ subjects:
Subject
Mathematics
Biology
Physics
Chemistry
Agricultural Science
Applied Mathematics
Physics & Chemistry
No. of Students
(2001, at all levels)
55144
24061
8411
6356
2915
1371
1023
Popularity
Rank
1
7
12
16
20
22
23
Size of cohorts in longitudinal studies:
Cohort
LCE 1996
LCE 1997
neither of these
Male
16443
9111
7841
Female
16776
11844
4993
Total
33219
20955
12834
Participation rates of the LCE 96 cohort in science subjects:
M
biology 35.1%
maths
99.8%
chemistry 13.5%
ph & ch 4.1%
physics 25.5%
app maths 3.4%
agr sc
8.9%
F
64.9%
99.9%
12.0%
1.6%
7.9%
0.4%
1.0%
Total
50.1%
99.9%
12.7%
2.8%
16.6%
1.9%
4.9%
F
62.5%
99.9%
13.0%
0.9%
9.5%
1.4%
0.9%
Total
51.5%
99.9%
13.7%
1.5%
16.5%
3.3%
3.0%
Participation rates of the LCE 97 cohort:
M
biology 37.2%
maths
99.8%
chemistry 14.6%
ph & ch 2.3%
physics 25.7%
app maths 5.9%
agr sc
5.7%
Whither Applied Mathematics at Leaving Certificate?
page 15
Participation rates in Applied Mathematics by school type:
LCE 96
sec
voc
comp
comm
all schools
H
2.22%
0.45%
1.06%
1.03%
1.67%
O
0.25%
0.09%
1.06%
0.05%
0.21%
population
21194
6892
849
4284
33219
LCE 97
sec
voc
comp
comm
all schools
H
3.67%
0.92%
4.04%
1.71%
3.06%
O
0.26%
0.03%
2.31%
0.19%
0.27%
population
15123
3150
520
2162
20955
Low achievement (grades E, F or NG) in science subjects:
LCE 96
maths
app maths
physics
chemistry
ph & ch
biology
agr sc
H
3.6%
8.1%
14.8%
13.3%
14.6%
12.5%
5.3%
O
15.3%
19.7%
22.4%
22.2%
34.5%
19.1%
26.4%
LCE 97
maths
app maths
physics
chemistry
ph & ch
biology
agr sc
H
2.8%
8.4%
10.2%
8.2%
8.3%
8.2%
4.0%
O
9.3%
7.1%
19.0%
13.6%
29.4%
14.2%
13.5%
Question 1: Does the choice of examination level depend on participation in the TYO?
H
O
96
555
71
626
97 (TYO)
642
56
698
1197
127
1324
Conclusion 1: There is some evidence for such dependence (p = 0.0416).
Whither Applied Mathematics at Leaving Certificate?
page 16
Question 2: Does participation in the TYO depend on gender?
96
97
M
551
538
1089
F
75
160
235
626
698
1324
Conclusion 2: The evidence for such dependence is overwhelming (p < 0.000001).
Question 3: For TYO participants, does choice of examination level depend on gender?
H
O
M
489
49
538
F
153
7
160
642
56
698
Conclusion 3: There is some evidence for such dependence (p = 0.0462).
Question 4: For TYO non-participants, does choice of examination level depend on
gender?
H
O
M
486
65
551
F
69
6
75
555
71
626
Conclusion 4: There is no evidence for such dependence (p = 0.3406).
Low performance and choice of examination level – all AM students (p = 0.0362):
Low
Not low
H
99
1098
1197
O
18
109
127
117
1207
1324
Low performance and choice of examination level – AM students who took TYO
(p = 0.004559):
H
O
Low
45
14
59
Not low
510
57
567
555
71
626
Whither Applied Mathematics at Leaving Certificate?
page 17